Michel Chipot University of Zurich Title: Some issues in singular perturbations

Abstract: We would like to study the asymptotic behaviour in $\epsilon$ of the solution to elliptic equations which includes anisotropic cases as for instance $$ -\epsilon^2 \partial^2_{x_1} u_{\epsilon}- \partial^2_{x_2}u_{\epsilon} = f(x_1,x_2) \textrm{ in } \Omega $$ together with boundary conditions.